On some integral representations of groups and global irreducibility

Dmitry Malinin

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Arithmetic aspects of integral representations of finite groups and their irreducibility are considered with a focus on globally irreducible representations and their generalizations to arithmetic rings. Certain problems concerning integral irreducible two-dimensional representations over number rings are discussed. Let K be a finite extension of the rational number field and OK the ring of integers of K. Let G be a finite subgroup of GL(2, K), the group of (2 × 2)-matrices over K. We obtain some conditions on K for G to be conjugate to a subgroup of GL(2, OK).

Original languageEnglish
Pages (from-to)81-94
Number of pages14
JournalInternational Journal of Group Theory
Volume7
Issue number3
Publication statusPublished - Sep 2018
Externally publishedYes

Keywords

  • Arithmetic rings
  • Class numbers
  • Genera
  • Globally irreducible representations
  • Hilbert symbol
  • Number fields
  • Quaternions
  • Schur ring
  • Torsion points of elliptic curves

ASJC Scopus subject areas

  • Algebra and Number Theory

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